Refractive index ellipse

A spherullite is usually pictured as an array of lamellae radially disposed to one another and as a result is spherically birefringent. A spherullite has two unique refractive indices the radial (Ht) and the tangential ( t)- The refractive index ellipse can represent the variation in refractive index in the plane, where the length of the major axis of the ellipse is proportional to the maximum refractive index in the plane and the length of the minor axis is proportional to the minimum refractive index. If the larger refractive index is in the tangential direction, i.e. < rit, the spherulite is termed negative. Spherulites show a characteristic Maltese cross pattern with a maximum in the intensity in the direction at 45 ° to the polarizer/analyser pair. 

Figure 7.40 Origin of Maltese cross pattern from a negative spherulite. The orientations of the polarizer (P), the analyser (A) and the refractive index ellipses are shown.

It is customary to define a refractive index ellipsoid which becomes an ellipse in the plane. The lengths of the long axes of the refractive index ellipse are proportional to the maximum and the minimum... 

Figure 11.5 The influence of the orientation of refractive index ellipses with respect to the polarizer (P)/analyser (A) pair on the transmitted light through the analyser.

Rotation of the polarization plane (or the axes of the dichroic ellipse) by a small angle a occurs when the phases for the two circular components become different, which requires a difference in the refractive index n (Pearlman and Nguyen 1991). This effect is called circular birefringence. The change of optical rotation with wavelength is called optical rotary dispersion (ORD). 

Here, the ellipses ( ) denote the higher-order terms in Thus the spread of the wavepacket due to the nontrivial refractive index is... 

It is interesting to point out that the O-dependent refractive index, given in (5.28), geometrically describes an ellipse as illustrated in Figure 5.3. 

The optical properties of a birefringent material are shown by a surface called the index ellipsoid or indicatrix. The radial distance from the center to each point on this surface is proportional to the refractive index of light that has its electric displacement D in that radial direction. This is not the refractive index of light that is traveling in that direction. Cross sections of this surface are ellipses. The indicatrix of an isotropic material would be a sphere with circular cross sections. 

In the cross-section of an elliptical fiber, contours of constant refractive index are closed ellipses. If the contours all have the same eccentricity, the fiber... 

Since the optical indicatrix is circularly symmetric about the major axis n, one of the minor axes, n (n ) can be chosen such that it lies in a plane parallel to the polarizer-analyzer plane. Taking a cross-section through the optical indicatrix gives an ellipse whose major axis is n and minor axis is the remaining n (fIj)- As shown in Fig. 6, the refractive index in the polarizer-analyzer plane n is given by the elliptical formula... 

If the optically active medium is not transparent at the wavelength of the incident radiation, the transmitted intensity may be further reduced by an absorptive contribution to the index of refraction. Because of preferential absorption of either the left or the right circularly polarized component, the emerging beam would no longer be the sum of equal amplitudes and trace out an ellipse with ellipticity tp = (kt — kr). Practical details of the measurement and chemical applications of optical activity are discussed by Charney[34],... 

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